Way back in January, Barack Obama asked his health-care advisers for a simple number. "I want to know how clearly and how unequivocally I can tell the American people their costs are going down when this is done," he said, according to someone at the meeting. During the campaign, Obama had promised to "lower health-care costs by $2,500 for the typical family," helping him make the sale on Election Day; the question, he knew, was going to be whether he could deliver on that specific number. (Watch Obama's speech to a joint session of Congress on Sept. 9, 2009.)

It has not been easy. His advisers told him the number, based on unproven assumptions, was too wobbly to survive a legislative debate. The truth was, they said, nobody knows exactly how much money could be saved by reforming health-care-delivery systems, as Obama and both houses of Congress have proposed. All they knew was that such reforms, which aim to restructure payment systems, decrease costs and increase the quality of care, are the only promising path forward to save the country from fiscal Armageddon. "You have never done it before, so how are you going to quantify it?" says Peter Orszag, a health-care wonk who runs the Office of Management and Budget. "The irony is that things that are more challenging to quantify precisely may well turn out to be much more important."

And so as Obama has barnstormed the country this year, he has been forced to talk more about the problem  a health-care inflation that could bankrupt the nation  than how much Americans would save if the broken system were fixed. From the Sunday news shows to David Letterman's overstuffed chair, Obama has warned about the rocketing increase in health-care insurance  5.5% last year, according to one study  and promised to bend the cost curve down in the future. He has described changes to the health-care system that could bring down costs for families and long-term government deficits. But his numbers are hypothetical. "If we are able to slow the growth of health-care costs by just one-tenth of 1% each year," he announced in a recent address to Congress, "it will actually reduce deficits by $4 trillion over the long term." (See pictures of the angry health-care debates.)

But are such savings ever likely to be realized? The answer, according to a wide range of experts, is frustratingly vague: Maybe. Hopefully. Probably. "Three-quarters of all the experts believe it is possible," says Harvard's David Cutler, a health-reform expert who has advised Obama. "What guarantees do we have? We don't." The reason for this ambiguity can be found in the nature of what Orszag calls the "transformational" changes. Policies in both the House and Senate versions of health reform seek nothing less than a remaking of the entire health-care industry  tying payments to outcomes, encouraging providers to work together, investing heavily in research to uncover which treatments work better than others and building a network to track the performance of individual doctors and regional health networks.

Most of these changes cannot be "scored" by accountants as yielding savings, since no one knows exactly how the system will respond to the new rules. Will doctors and hospitals revolt en masse against the changes? Will improved treatment really lead to a significant drop in unneeded procedures? "You need to give things a chance to change," explains Joseph Aslop, a health adviser for the Congressional Budget Office (CBO). "If you put [the pressure] on too hard too fast, things are going to break." (See 10 players in health-care reform.)

So when it comes to counting savings, the Obama team has been forced to rely in public on little more than crossed fingers. Meanwhile, in the backrooms of Congress, the assumptions have become fierce points of contention, as health-care providers lobby to keep the bill from shrinking payments in a way that would further stress the system. "Cost is driving the politics of health care more than anything else," says former South Dakota Senator Tom Daschle, who has been advising both Obama and the health-insurance industry. "The problem is that obviously there is a tremendous pushback by the people affected." (See 10 health-care-reform fight ads.)

So far, the Senate Finance Committee has shown much more determination than House Democrats in holding the fiscal line. According to the official government accounting, which leaves out most of the systemic changes, the current House bill would moderately grow the deficit over the next 20 years, while the Senate Finance Committee bill would save nearly $1 trillion in the same period.

Hanging over the debate are the hard facts of the U.S. government's grim fiscal prognosis. According to the CBO, federal spending on Medicare and Medicaid is projected to quintuple, from 4% of the economy in 2007 to 19% in 2082, if nothing changes. At the same time, the government is projected to run unsustainable deficits larger than the growth in the economy for the foreseeable future.

And so the President is left with a difficult task, like a salesman without a shiny car on the lot to show off. He is not exactly telling people to trust him  the theories behind the proposed cost savings are well documented. But he is promising something that cannot be demonstrated just yet, so instead of using the number he originally did, he has now settled on phrases like "It's going to start driving down our costs over the long term."